I have two Likert-scale variables, that values vary from "strongly disagree" to "strongly agree". Somehow I know, that many people who stronly disagree on the first scale, strongly agree on the second one (and the other way round). People who are moderate on one scale, they are also moderate on the other scale.
So my question is: is there any way to measure a curvilinear relationship between ordinal variables?
My data set is:
matr = matrix(c(19,21,35,19,13, 16,28,60,24,12, 27,39,54,53,32, 43,52,32,46,48, 54,48,29,45,50), 5,5)
Kendall's tau coef. is: 0.0097, which misleadingly indicates no relationship.
[UPDATE]: I'm aware that "curvilinear" in these Likert-scales case is a big word, but I see the pattern in the form "U", when I plot counts. The shoulders of "U" are those people, who "stronly disagree"/"strongly agree" with statement A and "stronly agree" with statement B. Others are moderate in both statements (the lower part of "U").